Question

name: olexia smarthour: 6m6.1 - perpendicular bisectors · spiral reviewfind the measure of each line segment4. kl5. tp6. kl

Explanation:

Step1: Use Perpendicular Bisector Theorem

For segment $KL$ (problem 4): The line through $M$ is the perpendicular bisector of $RL$, so $KR=KL$. Given $KR=4.2$, so $KL=4.2$.

Step2: Use Perpendicular Bisector Theorem

For segment $TP$ (problem 5): The line through $J$ is the perpendicular bisector of $LP$, so $TL=TP$. Given $TL=7$, so $TP=7$.

Step3: Use Perpendicular Bisector Theorem

For segment $KL$ (problem 6): The line through $K$ is the perpendicular bisector of $JL$, so $MJ=ML$. Given $ML=12$, so $KL$ is a segment on the perpendicular bisector, and since $MJ=ML=12$, $KL$ is not the equal segment here—wait, correction: The perpendicular bisector of $JL$ passes through $K$, so $MJ=ML=12$, and $KL$ is a segment from $K$ to $L$, but since $MK$ is the perpendicular bisector, $JL$ is split into two equal parts, so $KL$ is equal to $KJ$, but given $ML=12$, $KL$ is not the bisected segment, no—wait, the problem says find $KL$, and since $ML=12$, and $MK$ is the perpendicular bisector, $JL=2\times ML=24$? No, no: The perpendicular bisector theorem states that a point on the perpendicular bisector is equidistant from the endpoints. So point $M$ is on the perpendicular bisector of $JL$, so $MJ=ML=12$. But we need $KL$? Wait no, the label: $JL$ is the segment, $K$ is on the perpendicular bisector, so $KJ=KL$. Wait, no, the diagram shows $ML=12$, so $MJ=12$, and $KL$ is equal to $KJ$, but we don't have $KJ$, wait no—wait, no, the problem 6 says find $KL$, and the perpendicular bisector of $JL$ is the line through $K$, so $KL=KJ$, but $ML=12$, so $JL=24$, but no, $KL$ is not $JL$. Wait, no, I misread: The segment $JL$ has perpendicular bisector through $K$, so $MK$ is the perpendicular bisector, so $JK=LK$, and $JL$ is split into $JK=KL$? No, no, the perpendicular bisector splits $JL$ into two equal parts at $K$, so $JK=KL$, and $JL=12$, so $KL=\frac{12}{2}=6$. Oh right! The entire segment $JL$ is 12, split by the perpendicular bisector at $K$, so $KL=6$.

Wait correction for step 3:

Step3: Split segment by perpendicular bisector

The perpendicular bisector divides $JL=12$ into two equal parts, so $KL=\frac{12}{2}=6$.

Answer:

1. $KL = 4.2$
2. $TP = 7$
3. $KL = 6$